Irreducible restrictions of Brauer characters of the Chevalley group G2(q) to its proper subgroups

Abstract

Let G 2 (q) be the Chevalley group of type G 2 defined over a finite field with q = p n elements, where p is a prime number and n is a positive integer. In this paper, we determine when the restriction of an absolutely irreducible representation of G in characteristic other than p to a maximal subgroup of G 2 (q) is still irreducible. Similar results are obtained for 2 B 2 (q) and 2 G 2 (q).